The Seventh Dragon: The Riddle of Equal Temperament

by Anita T. Sullivan

A veteran piano tuner presents a non-technical, literary view of the quixotic tuning system used on keyboard instruments for hundreds of years. Winner of the Western States Book Award for creative non-fiction in 1986, newly updated with illustrations, index, bibliography.

Genres: Nonfiction

120 pages, Paperback

First published January 1, 1985

Reviews

[Warren · Rating 5 out of 5]

Pitch intervals sound most fulfilling if their frequencies are related by a ratio of small integers. For example, for an octave, the ratio of the frequency of the higher note to the lower note is 2:1. For a fifth, the ideal ratio is 3:2. For a tritone, the ideal ratio is 4:3. For a fourth, the ideal ratio is 5:4, and so on. For a half-step, the ideal ratio is 9:8. These intervals sound ideal to us because their higher harmonics align with and reinforce each other. Several styles of music, such as barbershop harmony, take advantage of this tendency for reinforcement to create chords that can only be described as thrilling.

It is a paradox, therefore, that if you start with the bottom note of an octave, and go up by 9:8 half-steps, you miss the top note of the octave. Specifically, (9/8)^12 > (2/1). If you wanted to go up by equal ratio half-steps, and reach 2:1 after the twelfth half-step, then you have to use a half-step ratio equal to the twelfth root of two, which is smaller than 9:8. Roughly, this is the interval that is used in most classical and orchestral music. [Something is wrong with my numbers. (9/8)^12 > (4/1). For some reason it is the sixth power, not the twelfth, that gives slightly more than 2:1.]

The author, a piano tuner by profession, focuses on the "comma", which is the pitch difference by which (9/8)^12 > (2/1), discusses its history, its importance in piano tuning, and philosophically what it all means.

[Joseph · Rating 5 out of 5]

I really liked this book that my sister sent me about tempering pianos. It's short, information specific (almost academic), and diligently prods the mysteries of music and listening. I've always had lots of questions about key theory and key tones but never received a complete answer. This was my complete answer--written well enough that even as I understood, it allowed the vastness of the incompleteness to consume me.

It also really made me really want to hear music in played in different (original) toning temperaments.

[Nick · Rating 4 out of 5]

There are a lot of people that have attempted to explain the tuning options that are out there. If you read them all, you start to get the picture. This short, elegant book concentrates on equal temperament and piano tuning, and contains a lot of tidbits that other explanations, however useful, don't mention.

[William · Rating 2 out of 5]

I suppose it isn’t that bad, it just is not what I expected or wanted at all. Should’ve looked harder at it. Less an elegantly written piece that is about tuning and more a set of essays more interested in repeating unanswerable questions and poetic language on the themes and ideas of piano tuning. Read it in just under an hour standing at work, but also spent $15 on it.